Initially indicted on marijuana trafficking, the case was reduced to a prohibited act relating to controlled substances.
He was given 200 hours of community service, fined $7,500 and ordered to undergo drug testing.
"I take full responsibility for my actions," Simpson said in court.
Simpson was a free agent before agreeing to his new deal with the Vikings, according to FOXSports.com's Jay Glazer.
Simpson, who played for the Cincinnati Bengals last year, caught 53 passes for 758 yards and four touchdowns for the season.
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